Si 2p and S 2p core-electron binding energies (CEBE)s of Si- and S-containing molecules were calculated by deMon DFT program using Slater’s transition-state (TS) concept. In the previous works, we could not obtain the calculated values to the experimental ones of third periodic 2p CEBEs for the molecules within the range of averaged absolute deviation (AAD) of 1.0eV, although the values were calculated by the unrestricted generalized transition-state (uGTS) method. Here, we were able to get the reasonable Si 2p and S 2p CEBEs of 11, and 12 gas molecules in the AAD of 0.37 and 0.46 eV, respectively from the CEBE calculations by the unrestricted generalized diffuse ionization (uGDI) method with a modification of screening constants for third periodic elements of the 2p core-hole. Furthermore, we estimated WD (work function and the other energies) values of seven Si- and S-containing polymers [(Si(CH3)(2))(n) (PDMS), (Si(CH3)(2)O)(n), (PDMSO), (Si(C6H5)CH3)(n) (PMPS), (Si(C6H5)CH3O)(n) (PPMSO), ((CH2CH2)S)(n) (PETHS), ((CH2(CH2)(4)CH2)SO2). (PHMS), ((C6H4)S)(n) (PPS)] from the differences between calculated CEBE values for the model molecules and experimental ones on the solid polymers.